Area and Hausdorff dimension of Sierpi\'{n}ski carpet Julia sets

We prove the existence of rational maps whose Julia sets are Sierpi'{n}ski carpets having positive area. Such rational maps can be constructed such that they either contain a Cremer fixed point, a Siegel disk or are infinitely renormalizable. We also construct some Sierpi'{n}ski carpet Julia sets with zero area but with Hausdorff dimension two. Moreover, for any given number $s\in (1,2)$, we prove the existence of Sierpi'{n}ski carpet Julia sets having Hausdorff dimension exactly $s$.